BRAID: Stream Mining through Group Lag Correlations.

The goal is to monitor multiple numerical streams, and determine which pairs are correlated with lags, as well as the value of each such lag. Lag correlations (and anti-correlations) are frequent, and very interesting in practice: For example, a decrease in interest rates typically precedes an increase in house sales by a few months; higher amounts of fluoride in the drinking water may lead to fewer dental cavities, some years later. Additional settings include network analysis, sensor monitoring, financial data analysis, and moving object tracking. Such data streams are often correlated (or anti-correlated), but with an unknown lag.We propose BRAID, a method to detect lag correlations between data streams. BRAID can handle data streams of semi-infinite length, incrementally, quickly, and with small resource consumption. We also provide a theoretical analysis, which, based on Nyquist's sampling theorem, shows that BRAID can estimate lag correlations with little, and often with no error at all. Our experiments on real and realistic data show that BRAID detects the correct lag perfectly most of the time (the largest relative error was about 1%); while it is up to 40,000 times faster than the naive implementation.